Suppose the null hypothesis, H0, is: a sporting goods store claims that at least 70% of its customers do not shop at any other sporting goods stores. What is the Type I error in this scenario? a. The sporting goods store thinks that less than 70% of its customers do not shop at any other sporting goods stores when, in fact, less than 70% of its customers do not shop at any other sporting goods stores. b. The sporting goods store thinks that at least 70% of its customers do not shop at any other sporting goods stores when, in fact, at least 70% of its customers do not shop at any other sporting goods stores. c. The sporting goods store thinks that less than 70% of its customers do not shop at any other sporting goods stores when, in fact, at least 70% of its customers do not shop at any other sporting goods stores. d. The sporting goods store thinks that at least 70% of its customers do not shop at any other sporting goods stores when, in fact, less than 70% of its customers do not shop at any other sporting goods stores.

A type of error I for this case would be reject the null hypothesis that the population proportion is greater or equal than 0.7 when actually is not true.

So the correct option for this case would be:

c. The sporting goods store thinks that less than 70% of its customers do not shop at any other sporting goods stores when, in fact, at least 70% of its customers do not shop at any other sporting goods stores.

Step-by-step explanation:

Previous concepts

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".

The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".

Type I error, also known as a “false positive” is the error of rejecting a null hypothesis when it is actually true. Can be interpreted as the error of no reject an alternative hypothesis when the results can be attributed not to the reality.

Type II error, also known as a "false negative" is the error of not rejecting a null hypothesis when the alternative hypothesis is the true. Can be interpreted as the error of failing to accept an alternative hypothesis when we don't have enough statistical power.

Solution to the problem

On this case we want to test if the sporting goods store claims that at least 70^ of its customers, so the system of hypothesis would be:

Null hypothesis: [tex]p \geq 0.7[/tex]

Alternative hypothesis: [tex]p<0.7[/tex]

A type of error I for this case would be reject the null hypothesis that the population proportion is greater or equal than 0.7 when actually is not true.

So the correct option for this case would be:

c. The sporting goods store thinks that less than 70% of its customers do not shop at any other sporting goods stores when, in fact, at least 70% of its customers do not shop at any other sporting goods stores.